Constant amplitude zero autocorrelation (CAZAC) sequences are increasingly used in new communication systems (e.g. LTE, WiMax). The (unique) Bjorck sequence whose length P is an odd prime is a less known CAZAC sequence. By modifying the Bjorck sequence through CAZAC transformations, a Bjorck set of P orthogonal sequences is introduced. The maximum absolute set cross-correlation is near 2/√P and the root-meansquare (RMS) of the cross-correlation function is 1/√P. A Bjorck set is contrasted with the widely used Zadoff-Chu set, which contains P−1 non-orthogonal sequences. The introduction of Bjorck sets gives a system designer more flexibility in sequence selection.